Continuing my story about big differences in depth of field (dof) between a p&s (large dof) and a DSLR (small dof) here's the first batch of shots to prove my point.
And the jury has already voted on this one: It's a draw between the Nikon DSLR (or any DSLR) and the Canon p&s (or any p&s for that matter). Why? Well, what you prefer (large or small dof) depends solely on your personal taste, your subject, and your "imaginary" goal.
And it is not necessarily so that the artful photographer always needs a small/shallow dof! Sometimes those guys go to great lengths to ensure maximum dof. They even buy very expensive special lenses (PC=perspective control for Nikon / TS=tilt&shift for Canon) to achieve this. All point&shooters can laugh at this as they have the larger than average dof already built in.

Now here's the proof (left=original clickable, right=100% crop):

D300@50/1.4

D300@50/4.8

870IS@13/4.5

Worlds apart, huh?!

Ok, I've added the DSLR at f/16 to see whether the dof can come close:
D300@50/16

Now the DSLR lens is stopped down almost 4 stops and still does not achieve a similar dof than the p&s!

Interesting... it made me try to play with a DoF calculator. The conclusion I came to is that there are too many variables. I can't come up with a simple statement on how much you need to stop down a low crop factor camera to get similar DoF for same FoV on a high crop factor camera. All I can say, it seems to be far more than "3-4 stops".

Taking the values above, a 13mm f/4.5 has a hyperfocal distance of around 223cm. That is, focused at that distance, things will appear acceptably sharp from approx 112cm away to infinity. To get the same hyperfocal distance at 50mm would need around f/28! And that doesn't cover that the out of focus characteristics will be different between them.

It's important that we don't take Thomas' thread off-topic but I tried to cover the DoF vs. sensor size issue in the opening post of my thread Full-frame Sensors Are Better - Fact or Fiction?. It was comparing cropped DSLR sensors and full frame sensors but the same logic extends to the really cropped sensors found in compact cameras.

I didn't intend to and don't think I took this OT. Simply putting some numbers to Thomas' statement made in the earlier post. Looking forward to seeing how it really works out in practice, never mind what the calculator says.

I didn't intend to and don't think I took this OT. Simply putting some numbers to Thomas' statement made in the earlier post. Looking forward to seeing how it really works out in practice, never mind what the calculator says.

Didn't mean to appear to make accusations. I wrote we meaning "you and I".

Ok, I've added a shot with the Nikon + 50mm lens at f/16 (!) to the above collection.
Conclusion: even stopping down the DSLR-lens 4 stops does not exactly give you the same dof on the p&s than on the DSLR. But it's close.

Now comes the real big challenge, shot in bright afternoon sun, color- and contrast-matched in Lightroom. These are 100% crops presented here in their full glory side-by-side as this vista cannot be composed at flickr directly or in your browser easily.
As usual these are screen-shots from Lightroom, so don't drill for any usable information in the meta-data of the images: You cannot cheat!

#1:

#2:

Close, isn't it? Even the dof Well, I choose this image specifically so you cannot find any differences in dof

I think the first one is from the 870, since in the second pics, you can find a little more detail in the back (forest). However, I actually prefer the first picture - probably because the 870 sharpens the image a little more by default.

I shoot only RAW with my D300. And to achieve the very best results I have to use the CaptureNX converter, which I did in this case.
Oops, sorry: My apologies go to the early viewers, who looked at only 50% crops with a RAW conversion from Lightroom.
Now I've uploaded 100% crops with the D300-images converted with CaptureNX. Sorry for this blunder So everybody may now vote again!